Question: Christopher is 12 years older than Ashley. Nineteen years ago, Christopher was 5 times as old as Ashley. How old is Ashley now?
Solution: We can use the given information to write down two equations that describe the ages of Christopher and Ashley. Let Christopher's current age be $c$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $c = a + 12$ Nineteen years ago, Christopher was $c - 19$ years old, and Ashley was $a - 19$ years old. The information in the second sentence can be expressed in the following equation: $c - 19 = 5(a - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to use our first equation for $c$ and substitute it into our second equation. Our first equation is: $c = a + 12$ . Substituting this into our second equation, we get the equation: $(a + 12)$ $-$ $19 = 5(a - 19)$ which combines the information about $a$ from both of our original equations. Simplifying both sides of this equation, we get: $a - 7 = 5 a - 95$ Solving for $a$ , we get: $4 a = 88$ $a = 22$.